Unit 4Section 4-5

4-5: Counting Rules To determine the number of possible outcomes for a

sequence of events we use one of three counting rules:

Fundamental Counting Rule

Permutation Rule

Combination Rule

Fundamental Counting Rule: In a sequence of n events in which the first one has k1 possibilities, the second one has k2 possibilities, and so forth…the total number of possibilities will be

k1 * k2 * k3 *…kn

(Multiply the possibilities)

Example 1: A coin is tossed and a die is rolled. Draw a tree diagram

to represent the total number of outcomes. Verify your findings using the fundamental counting rule.

Example 2: A paint manufacturer wishes to manufacture several

different paints. The categories include:

Color: red, blue, white, black, green, brown, yellow

Type: latex, oil

Texture: Flat, semigloss, high gloss

Use: Indoor, outdoor

How many different kinds of paint can be made if a person can select one color, one type, one texture, and one use?

Section 4-5

Example 3: The digits 0, 1, 2, 3, and 4 are to

be used in a four-digit ID card. How many different cards are possible if repetitions are permitted?

Section 4-5

Factorial Notation – uses an ! as its notation.

5! Means 5 * 4 * 3 * 2 * 1 Special Definition: 0! = 1

Example 4: Simplify 2! 4! (5 – 2)! 5! – 2 3! + 5!

Section 4-5

Homework: Pg 220 – 221: 1 – 12, 13 c, d, h, i

Section 4-5